Answer:
a. Scatterplot is attached.
b. Positive Correlation
c. Correlation coefficient=0.9219
Step-by-step explanation:
a.
The following procedure will be used to obtain the scatter plot
- Open an Google Sheets file online or excel sheet on your computer.
- In column B and C, enter the Income and Vacation data as provided above.
- Select the data > click on insert CHART.
- Chose Scatter Chart option
A scatter plot visualizing your data should be displayed as attached.
b.
- On your computer, open a spreadsheet in Google Sheets.
- Double-click on your scatter plot.
- At the right, click on Customize tab and then Series.
- Scroll down and check the Trend line box
-From the trend line, your notice that your variables have a positive correlation.
-As the income increases, so does vacation expenditure.
c. The correlation coefficient can be calculated as follows.
- Click on any empty cell in the sheet and enter the formula
- "=CORREL((y-axis range),(x-axis range))"
- ENTER
-From our Google Sheets calculation our variables have a positive correlation and the correlation coefficient is 0.9219
-The correlation coefficient,r can also be calculated manually:
-let x be income, and y be vacation and divide all the values by 100 to make the smaller and easier to manipulate:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2}}\\\\\\\sum xy=153914\\\sum x=4485\\\sum y=246\\\sum x^2=2878447\\(\sum x)^2=4485^2=20115225\\(\sum y)^2=246^2=60516\\\sum y^2=8392\\n=8\\\\\#substitute \ and \ solve \ for \ r\\\\=\frac{8\times153914-4485\times 246}{\sqrt{[8\times 2878447-4485^2][8\times 8392-246^2]}}\\\\=0.92186\\\\\approx 0.9219](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2-%28%5Csum%20y%29%5E2%7D%7D%5C%5C%5C%5C%5C%5C%5Csum%20xy%3D153914%5C%5C%5Csum%20x%3D4485%5C%5C%5Csum%20y%3D246%5C%5C%5Csum%20x%5E2%3D2878447%5C%5C%28%5Csum%20x%29%5E2%3D4485%5E2%3D20115225%5C%5C%28%5Csum%20y%29%5E2%3D246%5E2%3D60516%5C%5C%5Csum%20y%5E2%3D8392%5C%5Cn%3D8%5C%5C%5C%5C%5C%23substitute%20%5C%20and%20%5C%20solve%20%5C%20for%20%5C%20r%5C%5C%5C%5C%3D%5Cfrac%7B8%5Ctimes153914-4485%5Ctimes%20246%7D%7B%5Csqrt%7B%5B8%5Ctimes%202878447-4485%5E2%5D%5B8%5Ctimes%208392-246%5E2%5D%7D%7D%5C%5C%5C%5C%3D0.92186%5C%5C%5C%5C%5Capprox%200.9219)
Answer:
The sum of half of a number and three-fourths is at least five and one quarter
Step-by-step explanation:
It's all about making sense of an English sentence.
"half the sum ..." is different from "the sum of half ..."
And ...
"at least" and "not less than" mean the same (≥)
"not more than" and "at most" mean the same (≤)
_____
Since all of the expressions are written out in words, it is a matter of matching the ideas expressed. That's a problem in reading comprehension, not math.
__
"One-half x + three-fourths [is] greater-than-or-equal-to 5 and one-fourth"
means the same as ...
"The sum of half of a number and three-fourths is at least five and one quarter"
Let
x---------> represent the number of miles Troy's has driven
y--------> represent the amount of gas in Troy's truck
we know that
the equation that represents the amount of gas, y, in troy' s truck after driving a certain number of miles, x is

where
m is the slope---------> 
in this problem the slope is equal to 
it's negative because the tank is going to be consumed
assuming he starts with a full tank

substitute in the formula above

therefore
the answer is
the equation 
The answer is 8 ihinghkki
Step-by-step explanation:
1024 bytes = 1 kb
n kb = 1024 × n b
Where n is a positive number